Experimental characterization of coherent and non-Markovian errors using tangent space decomposition

TL;DR

This paper introduces a tangent-space decomposition method to accurately characterize and quantify coherent, Markovian, and non-Markovian errors in single-qubit gates on a trapped ion platform, improving error diagnosis in quantum devices.

Contribution

The paper presents a novel tangent-space decomposition technique for experimentally distinguishing and quantifying different error types in quantum gates, including non-Markovian effects.

Findings

Successfully applied to trapped ion qubits

Quantified non-Markovian effects from environmental fluctuations

Identified coherent miscalibrations in quantum control

Abstract

Accurate characterization of coherent and non-Markovian errors remains a central challenge in quantum information processing, as conventional benchmarking techniques typically rely on Markovian and time-independent noise assumptions. In practice, however, quantum devices exhibit both systematic coherent miscalibrations and temporally correlated fluctuations, which complicate error diagnosis and mitigation. Here, we apply a technique based on tangent-space decomposition to characterize such error in single-qubit quantum gates implemented on a trapped ion platform. Small imperfections in a quantum operation are treated as perturbations of the target quantum map, represented as tangent vectors in the space of quantum channels. This formulations enables a natural decomposition of the deviation into three components corresponding to coherent, Markovian and non-Markovian processes.The relative weights of these components provide a quantitative measure of the contribution from each type of error mechanism, directly from a single tomographic snapshot. We experimentally validate this method on a single-qubit gates implemented on a trapped $^{40}$Ca$^+$ ion, where control is achieved through laser-driven optical transitions. By analyzing experimentally reconstructed process matrices, expressed in the Pauli Transfer Matrix and Choi representations, we identify and quantify non-Markovian effects arising from controlled injection of slow fluctuations in the experimental environment. We also characterize deterministic coherent miscalibrations using the same technique. This approach provides a physically transparent and experimentally accessible tool for diagnosing complex error sources in quantum control systems.